Global existence for two extended Navier-Stokes systems

Ignatova, Mihaela, Iyer, Gautam, Kelliher, James P, Pego, Robert L and Zarnescu, Arghir D (2015) Global existence for two extended Navier-Stokes systems. Communications in Mathematical Sciences, 13 (1). pp. 249-267. ISSN 1539-6746

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Abstract

We prove global existence of weak solutions to two systems of equations which extend the dynamics of the Navier-Stokes equations for incompressible viscous flow with no-slip boundary condition. The systems of equations we consider arise as formal limits of time discrete pressure-Poisson schemes introduced by Johnston \& Liu {[}J. Comput. Phys. 199, 221-259, 20041 and by Shirokoff \& Rosales {[}J. Comput. Phys. 230, 8619-8646, 20111 when the initial data does not satisfy the required compatibility condition. Unlike the results of Iyer et al. {[}J. Math. Phys. 53, 115605, 20121, our approach proves existence of weak solutions in domains with less than regularity. Our approach also addresses uniqueness in 2D and higher regularity.

Item Type: Article
Keywords: Navier-Stokes; numerics; global well-posedness
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User: Arghir Zarnescu
Date Deposited: 13 Mar 2015 10:40
Last Modified: 13 Mar 2015 10:40
URI: http://sro.sussex.ac.uk/id/eprint/53361
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